Lehmer-Ramanujan Numbers

N. Lygeros, O. Rozier

Odd prime values of the Ramanujan tau function in The Ramanujan Journal , 15/03/2013- Pdf

LR Data.

|2cos(theta(p))|
p
q
size
primality

good/bad
numbers

Discovery
Program
Date
Contributors
Time Total CPU time
0.822567
251
3
26
P
very bad (13)
Lehmer 01
1965
Lehmer
0.381879
677
3
32
P
-
LR 02
2011
LR
0.798883
971
3
33
P
bad
LR 03
2011
0.413262
983
3
33
P
bad
LR 04
2011
1.709172
47
5
37
P
very good (11)
LR 05
2011
0.690618
197
5
50
P
-
LR 06
2011
0.149742
227
11
130
P
bad
LR 07
2011
0.962083
379
11
142
P
-
LR 08
2011
1.600770
829
11
161
P
-
LR 09
2011
1.229474
607
13
184
P
-
LR 10
2011
1.099902
761
13
190
P
-
LR 11
2011
1.162514
29
31
242
P
-
LR 12
2011
0.716263
281
19
243
P
-
LR 13
2011
0.084978
439
29
407
P
-
LR 14
2011
1.709172
47
47
424
P
-
LR 15
2011
1.216486
947
41
654
P
-
LR 16
2011
1.162514
29
83
660
P
-
LR 17
2011
0.508967
811
43
671
P
bad
LR 18
2011
1.153966
613
47
706
P
very bad (17)
LR 19
2011
0.474429
89
73
772
P
very good (29)
LR 20
2011
0.642521
401
59
831
P
-
LR 21
2011
1.747589
937
59
949
P
-
LR 22
2011
0.314073
977
59
954
P
-
LR 23
2011
1.452457
773
67
1049
P
-
LR Titan 24
gp
2011
0.701505
503
73
1070
P
very good (29)
LR Titan 25
gp
2011
1.561722
787
73
1147
P
-
LR Titan 26
gp
2011
0.466280
173
103
1256
P
-
LR Titan 27
gp
2011
0.630563
421
89
1271
P
-
LR Titan 28
gp
2011
0.890666
223
101
1292
P
-
LR Titan 29
gp
2011
0.592221
239
107
1387
P
-
LR Titan 30
gp
2011
0.148174
557
109
1631
P
-
LR Titan 31
gp
2011
1.000872
11
317
1810
P
very bad (11)
LR Titan 32
gp
2011
1.162514
29
229
1834
P
-
LR Titan 33
gp
2011
0.434747
113
197
2214
P
good
LR Titan 34
gp
2011
0.568639
809
149
2367
P
very good (11)
LR Titan 35
gp
2011
0.765198
491
167
2457
P
-
LR Titan 36
gp
2011
1.179650
17
433
2924
P
-
LR Titan 37
gp
2011
0.241885
353
239
3335
P
-
LR Titan 38
gp
2011
0.886942
97
331
3606
P
-
LR Titan 39
gp
2011
31h
0.890666
223
281
3617
P
-
LR Titan 40
gp
2011
32h
0.268015
881
241
3888
P
very good (11)
LR Titan 41
primo
16/04/2013
Gérasimos
29h
59h
0.268015
881
251
4050
P
-
LR Titan 42
primo
16/04/2013
Neoklis
29h
29h
0.457445
109
373
4169
P
-
LR Titan 43
primo
16/04/2013
Olivier
11h
46h
0.630563
421
317
4561
P
-
LR Titan 44
primo
17/04/2013
Neoklis
21h
41h
1.541981
941
349
5692
P
good
LR Titan 45
primo
28/04/2013
Gérasimos
0.265111
349
409
5706
P
-
LR Titan 46
primo
19/04/2013
Olivier
44h
174h
0.363777
487
479
7066
P
-
LR Titan 47
primo
25/04/2013
Neoklis
7d
13d
0.798883
971
433
7098
P
very bad (11)
LR Titan 48
primo
20/05/2013
Dimitris
1.583644
449
547
7965
P
-
LR Titan 49
primo
23/05/2013
Olivier
5d
35d
1.649726
953
557
9111
P
good
LR Titan 50
primo
05/08/2013
Theodora
0.886942
97
887
9682
P
-
LR Titan 51
primo
26/05/2013
Keira
1.644580
857
683
11002
P
-
LR Giant 52
primo
20/07/2013
Socratis
0.944962
59
1381
13441
P
very good (11)
LR Giant 53
primo
12/10/2013
Gérasimos
83d
326d
0.109065
643
953
14703
P
-
LR Giant 54
FastECPP
01/02/2011
François
13d
313d+42d
1.153966
613
1013
15515
P
-
LR Giant 55
primo
02/09/2014
Kostas/Keira
0.822567
251
1193
15733
pp
very bad (11)
LR Giant
primo
failed
Keira
1.323747
673
1019
15834
P
-
LR Giant 56
primo
19/06/2013
Patrice
30d
892d
1.393695
79
1571
16386
P
-
LR Giant 57
primo
07/02/2014
Gérasimos
0.987446
571
1091
16526
P
-
LR Giant 58
primo
05/12/2013
Dimitris
1.441636
587
1093
16629
pp
good
LR Giant
primo
Neoklis
0.026114
821
1163
18626
P
-
LR Giant 59
primo
04/07/2014
Keira
1.868850
619
1297
19900
P
very good (17)
LR Giant 60
primo
07/08/2014
Patrice
0.415345
41
2297
20367
pp
very bad (11)
LR Giant
primo
failed
Patrice
1.333141
257
1699
22506
P
-
LR Giant 61
primo
23/04/2014
Patrice
180d
4573d
0.663405
691
1523
23770
P
-
LR Giant 62
primo
27/02/2014
André, Philippe & Pierre
238d
7179d
1.100312
157
2207
26643
P
-
LR Giant 63
FastECPP
03/04/2011
François
59d
1963d+392d
0.879617
331
2129
29492
P
-
LR Giant 64
primo
15/09/2015
André, Philippe & Pierre
559d
17888d
1.709172
47
4177
38404
pp
very good (11)
LR Giant
1.403115
739
2503
39475
pp
-
LR Giant
0.266890
463
2753
40347
pp
-
LR Giant
1.631383
461
3019
44215
pp
-
LR Giant
0.165452
199
4519
57125
pp
good
LR Super Giant
1.829136
877
3617
58531
pp
-
LR Super Giant
1.644580
857
3847
62042
pp
-
LR Super Giant
0.890722
409
4423
63520
pp
-
LR Super Giant
1.393695
79
6317
65920
pp
-
LR Super Giant
0.661184
839
4177
67153
pp
very good (17)
LR Super Giant
0.944962
59
8971
87365
pp
very good (11)
LR Super Giant
0.568639
809
6029
96410
pp
-
LR Super Giant
     
0.890666
223
9431
121795
pp
-
LR Hyper Giant
1.462783
317
10331
142098
pp
-
LR Hyper Giant
     
1.918814
103
14939
165374
pp
-
LR Hyper Giant
0.109065
643
11689
180524
prp
-
LR Hyper Giant
     
0.395585
373
15187
214796
prp
-
LR Hyper Giant
     
0.972080
311
15787
216429
pp
-
LR Hyper Giant
     
0.972080
311
16453
225560
pp
-
LR Hyper Giant
     
0.415345
41
28289
250924
pp
very good (19)
LR Hyper Giant
     
0.798883
971
15739
258571
pp
good
LR Hyper Giant
     
0.111250
509
18947
282048
pp
-
LR Hyper Giant
0.004564
907
20849
339132
pp
-
LR Hyper Giant
0.768786
863
24631
397727
pp
-
LR Hyper Giant
1.696603
631
32371
498503
pp
-
LR Hyper Giant
     
1.452000
773
34961
555339
pp
-
LR Hyper Giant
     
0.268015
881
38993
631568
pp
-
LR Hyper Giant
     
0.413262
983
38933
640784
pp
-
LR Hyper Giant
     


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